A significant part of everyday learning occurs incidentally — a process typically described as implicit learning. A central issue in this domain and others, such as language acquisition, is the extent to which performance depends on the acquisition and deployment of abstract rules. Shanks and colleagues [22], [11] have suggested (1) that discrimination between grammatical and ungrammatical instances of a biconditional grammar requires the acquisition and use of abstract rules, and (2) that training conditions — in particular whether instructions orient participants to identify the relevant rules or not — strongly influence the extent to which such rules will be learned. In this paper, we show (1) that a Simple Recurrent Network can in fact, under some conditions, learn a biconditional grammar, (2) that training conditions indeed influence learning in simple auto-associators networks and (3) that such networks can likewise learn about biconditional grammars, albeit to a lesser extent than human participants. These findings suggest that mastering biconditional grammars does not require the acquisition of abstract rules to the extent implied by Shanks and colleagues, and that performance on such material may in fact be based, at least in part, on simple associative learning mechanisms.